Many phenotypes of interest, including the susceptibility to many common diseases, are quantitative, in that the heritable variation in the trait is largely due to many genetic variants of small effects segregating in the population. The causes of quantitative genetic variation have been pursued in evolutionary biology for over a century. This pursuit has recently come to the forefront of research in human genetics as well, with the push to map the variants that underlie heritable genetic variation in disease risk. Since 2007, genome-wide association studies (GWAS) in humans have led to the identification of thousands of variants reproducibly associated with hundreds of quantitative traits, including susceptibility to a wide variety of diseases. These studies reveal intriguing differences among traits in their genetic architecture (i.e., the number of associated variants, their effect sizes ad frequencies) and in the fraction of the heritable variation explained (i.e., the missing heritabilty problem). Interpreting these findings has been difficult, however, because of the lack of models for how evolutionary processes give rise to genetic architecture. Similarly, recent population genetic studies in humans, Drosophila and other species indicate that many, if not most, adaptations may involve a polygenic response. Yet our understanding of polygenic adaptation is stymied by the lack of models that relate directional selection on quantitative traits to their underlying genetic architecture. We propose to marry approaches from evolutionary biology and findings in human genetics in order to learn about the evolutionary processes that shape quantitative genetic variation and polygenic adaptation in humans. In Aim 1, we will model how population genetic parameters, notably of stabilizing selection and pleiotropy, shape the genetic architecture of quantitative traits. This will provide a much-needed framework for interpreting differences in architecture and missing heritability among traits. In Aim 2, we will develop a likelihood method to infer the evolutionary parameters underlying the genetic architecture of traits from GWAS data, and apply it to range of (at least 12) human traits. From these inferences, we will learn how architecture varies among traits, e.g., between complex diseases and anthropomorphic traits, and more generally about the forces that maintain quantitative genetic variation. We will also use these inferences to guide the design of future mapping strategies. In Aim 3, we will model how genetic architecture and pleiotropy shape the response to novel selection pressures on quantitative traits. We will characterize the signatures of polygenic adaptation in polymorphism data (notably in terms of population differentiation and diversity levels) and assess the power of methods that combine the weak signals across individual loci to detect selection on quantitative traits. This work will help to identify polygenc adaptation in humans, as well as in other species. The proposed research should thus fill fundamental gaps in our understanding of natural selection on quantitative traits, and provide an important set of models and tools for further studies in both human and evolutionary genetics.